Step by step
The question
Question: find the prime factors of 126.
Prime factors of 126
A prime number has exactly two factors: 1 and itself.
Like 2, 3, 5, 7 and 11.
We want 126 as primes multiplied together.
prime: only 1 × itself
2, 3, 5, 7, 11, 13, ...
1 Make a factor tree
2 Collect the primes
We collect the circled numbers, smallest first.
= 126 = 2 × 3 × 3 × 7
3 shows up 2 times.
So 3 times 3 is written 3 squared.
= 126 = 2 × 32 × 7
3 Check
Let's check: we multiply them back.
2 times 3 is 6.
6 times 3 is 18.
18 times 7 is 126.
2 × 3 = 6, 6 × 3 = 18
18 × 7 = 126
We get 126 again.
So it is right!
Let's look back.
First: make a factor tree.
Then: collect the primes.
Last: check.
Answer
= 126 = 2 × 32 × 7